Question #c1e7f

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Answer 1 · 2016-05-11T14:01:52

k = $\frac{21}{8}$ $21/8$ or $2.625$ $2.625$

We have
$\frac{2}{3} + 8 \frac{k}{4} = \frac{71}{12}$ $2/3 + 8k/4 = 71/12$

Subtract 2/3 from both sides
$(\frac{2}{3} - \frac{2}{3}) + 8 \frac{k}{4} = \frac{71}{12} - \frac{2}{3}$ $(2/3 - 2/3) + 8k/4 = 71/12 - 2/3$

Write 2/3 as 8/12 (multiply 4 in both numerator and denominator)

$8 \frac{k}{4} = \frac{71}{12} - \frac{8}{12}$ $8k/4 = 71/12 - 8/12$

Take $\frac{1}{12}$ $1/12$ common

$8 \frac{k}{4} = (71 - 8) \times \frac{1}{12}$ $8k/4 = (71-8)xx1/12$

Divide by 2 on both sides
$8 \frac{k}{4 \times 2} = \frac{1}{2} \times \frac{63}{12}$ $8k/(4xx2) = 1/2 xx 63/12$

You have
$cancel(8)k/cancel(8) = 63/24$

k = 63/24

Divide by both numerator and denominator by 3

$k = (63/3)/(24/3)$

$k = 21/8$ or $2.625$